Math  /  Geometry

QuestionWrite the coordinates of the vertices after a translation 5 units left and 10 units down. S(IS^{\prime \prime}(I , \square \square ) T(T^{\prime}( \square \square uu^{\prime} \square , \square v=v^{\prime \prime}= \square

Studdy Solution

STEP 1

What is this asking? We're taking a rectangle on a graph and sliding it 5 units to the left and 10 units down!
Then, we need to find the new coordinates of the corners. Watch out! Don't mix up left/right with up/down!
Left means *smaller* x-values, and down means *smaller* y-values.

STEP 2

1. Shift the x-coordinates
2. Shift the y-coordinates
3. Write the new coordinates

STEP 3

Alright, let's **slide those x-coordinates** 5 units to the left!
Remember, "left" means we're *subtracting* from the x-value.

STEP 4

Our **original** x-coordinate for S is 22.
Moving 5 units left gives us 25=32 - 5 = \mathbf{-3}.
So, the new x-coordinate for S' is 3\mathbf{-3}!

STEP 5

T also starts at x=2x = 2.
Moving 5 to the left gives us 25=32 - 5 = \mathbf{-3}.
The new x-coordinate for T' is also 3\mathbf{-3}!

STEP 6

U starts at x=8x = 8.
Sliding 5 to the left: 85=38 - 5 = \mathbf{3}.
U' has an x-coordinate of 3\mathbf{3}!

STEP 7

Finally, V starts at x=8x = 8.
Moving 5 left: 85=38 - 5 = \mathbf{3}.
V' has an x-coordinate of 3\mathbf{3}!

STEP 8

Now, let's **shift those y-coordinates** 10 units down! "Down" means we *subtract* 10.

STEP 9

S starts at y=0y = 0.
Moving 10 down: 010=100 - 10 = \mathbf{-10}.
S' has a y-coordinate of 10\mathbf{-10}!

STEP 10

T starts at y=6y = 6.
Moving 10 down: 610=46 - 10 = \mathbf{-4}.
T' has a y-coordinate of 4\mathbf{-4}!

STEP 11

U starts at y=6y = 6.
Moving 10 down: 610=46 - 10 = \mathbf{-4}.
U' has a y-coordinate of 4\mathbf{-4}!

STEP 12

V starts at y=0y = 0.
Moving 10 down: 010=100 - 10 = \mathbf{-10}.
V' has a y-coordinate of 10\mathbf{-10}!

STEP 13

Let's put it all together!
We shifted our x's to the left and our y's down.
Now we have the **new coordinates**!

STEP 14

S' is at (3,10)(\mathbf{-3}, \mathbf{-10}).

STEP 15

T' is at (3,4)(\mathbf{-3}, \mathbf{-4}).

STEP 16

U' is at (3,4)(\mathbf{3}, \mathbf{-4}).

STEP 17

V' is at (3,10)(\mathbf{3}, \mathbf{-10}).

STEP 18

S(3,10)S'(-3, -10) T(3,4)T'(-3, -4) U(3,4)U'(3, -4)V(3,10)V'(3, -10)

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